Question 707044: We had this problem at school with no help in solving. I did it by trial and error but don't know the actual formula for solving.
The equation was: N(four digits)/D(one digit)=1234 r5.
Any help on how to solve for both N and D? Thanks!
Raphael
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! You have a few numbers of only 1 digit length to choose from and test. Your choices to try are from the set, {2,3,4,5,6,7,8,9}. Those are the possible divisors to test.
N/D=1234r5, same as N/D=1234+5/D.
Multiply both sides by D:
 .
Test all the possible denominators of whole numbers from 2 to 9. Some are going to be better than others. I would suggest D greater than 5. 6, 7, and 8 work well. 9 will NOT work, giving a five-digit number.
Some what found:
D____________N
6____________7409
7____________8643
8____________9877
9____________11111, which is too many digits. We wanted four; not more than.
The difficulty with choosing D=5 is that we want our remainder to actually BE 5.
Look... 1234*5+5/5=6175, and that 6175/5=1235 which in truth is not something that really gives a remainder upon 1234. 5/5 is NOT really a remainder.
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